Practice questions
88551 published questions with worked solutions.
- The function f : (- , ) (-1,1), defined by f(x)= 2^x-2^ -x 2^x+2^ -x is :
- If > > > 0, then the expression ^ -1 + (1+ ^2) ( - ) + ^ -1 + (1+ ^2) ( - ) + ^ -1 + (1+ ^2) ( - ) is equal to :
- Let f : (0, ) R be a function which is differentiable at all points of its domain and satisfies the condition x^2f'(x) = 2xf(x) +...
- Let A = x (0, )- 2 : _ (2/ ) | x| + _ (2/ ) | x| = 2 and B = x 0 : x ( x -4)-3| x -2|+6=0 . Then n(A B) is equal to :
- Let [x] denote the greatest integer function, and let m and n respectively be the numbers of points, where the function f(x) =...
- In an arithmetic progression, if S_ 40 = 1030 and S_ 12 = 57, then S_ 30 - S_ 10 is equal to :
- If 7 = 5 + 1 7 (5+ ) + 1 7^2 (5+2 ) + 1 7^3 (5+3 ) + , then the value of is :
- If the system of equations x + 2y - 3z = 2 2x + + 5z = 5 14x + 3y + = 33 has infinitely many solutions, then + is equal to :
- Let (2, 3) be the largest open interval in which the function f(x) = 2 _e(x - 2) - x^2 + ax + 1 is strictly increasing and (b, c)...
- Suppose A and B are the coefficients of 30th and 12th terms respectively in the binomial expansion of (1+x)^ 2n-1 . If 2A = 5B,...
- Let a = 3 i - j +2 k , b = a ( i -2 k ) and c = b k . Then the projection of c -2 j on a is :
- For some a, b, let f(x) = vmatrix a+ x x & 1 & b a & 1+ x x & b a & 1 & b+ x x vmatrix , x 0, _ x 0 f(x) = + a + b. Then ( + +...
- Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can...
- Let A = [a_ ij ] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix....
- If the equation of the parabola with vertex V ( 3 2 ,3 ) and the directrix x + 2y = 0 is x^2 + y^2 - xy - 30x - 60y + 225 = 0,...
- Number of functions f : 1, 2, , 100 0, 1 , that assign 1 to exactly one of the positive integers less than or equal to 98, is...
- Let P be the image of the point Q(7, -2, 5) in the line L : x-1 2 = y+1 3 = z 4 and R(5, p, q) be a point on L. Then the square...
- Let y = y(x) be the solution of the differential equation 2 x dy dx = 2x - 4y x, x (0, 2 ). If y ( 3 )=0, then y' ( 4 )+y ( 4 )...
- Let H_1 : x^2 a^2 - y^2 b^2 =1 and H_2 : x^2 A^2 + y^2 B^2 =1 be two hyperbolas having length of latus rectums 15 2 and 12 5...
- If 2x^2+5x+9 x^2+x+1 dx = x x^2+x+1 + x^2+x+1 + _e |x+ 1 2 + x^2+x+1 | + C, where C is the constant of integration, then + 2 is...